A048978 Light numbers, those whose mean sum of divisors <= mean running sum of divisors of all previous n.

360, 630, 720, 840, 900, 960, 1008, 1080, 1120, 1200, 1260, 1320, 1344, 1400, 1440, 1512, 1540, 1560, 1584, 1620, 1680, 1728, 1760, 1800, 1848, 1872, 1890, 1920, 1980, 2016, 2040, 2100, 2112, 2160, 2184, 2240, 2268, 2280, 2310, 2340, 2352, 2376, 2400

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Keep running totals of sum, rs and number of divisors, rd, for all numbers to n-1. Divide rs by rd. If mean at n <= running mean at n-1, then number is "light, " else "heavy."

Example

a(1)=360. At 360 rs/rd of all previous n is 105811/2162=48.94+. At 360, s/d is 1170/24=48.75. 48.75<=48.94 so 360 is "Light."

Mathematica

t = {1, 1}; seq = {}; Do[s = DivisorSigma[#, n] & /@ {0, 1}; If[s[[2]]/s[[1]] < t[[2]]/t[[1]], AppendTo[seq, n]]; t += s, {n, 2, 2400}]; seq (* Amiram Eldar, Sep 06 2019 *)

Crossrefs

Cf. A000005, A000203.

Sequence in context: A163569 A063067 A076205 * A056502 A056492 A158308

Adjacent sequences: A048975 A048976 A048977 * A048979 A048980 A048981

Keyword

easy,nonn

Author

Enoch Haga

Extensions

a(22) corrected by Amiram Eldar, Sep 06 2019

Status

approved